Finite Group Databasebeta

← C3×D51⋊(C7⋊D7) #44472953

Subgroups — C3×D51⋊(C7⋊D7) #44472953

Order 29988.

440 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7⋊D119C211yesmaximal, characteristic, complemented
2C3×C72×D51C211yesmaximal, characteristic, complemented
3C3×C17×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D51⋊(C7⋊D7)C311yesmaximal, characteristic, direct product factor
5C3×D17×C7⋊D7—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C17×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D51C2×C311yescharacteristic, complemented
9C3×C7⋊D119—21no—
10C3×C7⋊D119D311yescharacteristic, complemented
11C3×C7⋊D119C2×C311yescharacteristic, complemented
12C3×C17×C7⋊D7—31no—
13C3×C72×D17—31no—
14C3×D21⋊D17—78nomaximal
15D17×C7⋊D7—31noHall
16C3×C72×C17—21no—
17C3×C72×C17C2×D311yescharacteristic, complemented
18C3×C72×C17C22×C311yescharacteristic, complemented
19C3×C17×D21—78no—
20C3×C7×D51D718yescomplemented
21C32×D119—78no—
22C3×D3×C7⋊D7—171nomaximal, Hall
23C7⋊D119C3×D311yescharacteristic, complemented
24C17×C7⋊D7—31no—
25C72×D17—31no—
26D21⋊D17—78no—
27C3×D7×D17—218no—
28C32×C7×C17C2×D718yescomplemented
29C3×C3⋊(C7⋊D7)D1711yescharacteristic, complemented
30C3×D3×C72—171no—
31C32×C7⋊D7—171no—
32C72×C17C2×C3×D311yescharacteristic, complemented, Hall
33C17×D21—78no—
34C7×D51C3×D718yescomplemented
35C3×D119—78no—
36C3×D119—78no—
37C3×D119—148no—
38C3×D7×C17—218no—
39C3×C7×D17—38no—
40C3×D3×D17—491noHall
41C2×C3×C7⋊D7—511no—
42D3×C7⋊D7—171no—
43D7×D17—218no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—28no—
46C3×C7×C17D3×D718yescomplemented
47C3×C7×C17C2×C3×D718yescomplemented
48C3×D51C7⋊D711yescharacteristic, complemented
49C3×D3×C17—491no—
50C32×D17—491no—
51C2×C3×C72—511no—
52C3⋊(C7⋊D7)C3×D1711yescharacteristic, complemented
53D3×C72—171no—
54C3×C7⋊D7—31no—
55C3×C7⋊D7—171no—
56C3×C7⋊D7—171no—
57C3×C7⋊D7—341no—
58C3×D3×D7—1198no—
59D119—78no—
60C7×D17—38no—
61D7×C17—218no—
62C2×C3×D17—1471no—
63D3×D17—491no—
64C2×C7⋊D7—511noHall
65C32×C17C2×C7⋊D711yescharacteristic, complemented, Hall
66C3×C72—21no—
67C3×C72D3×D1711yescharacteristic, complemented
68C3×C72C2×C3×D1711yescharacteristic, complemented
69C3×D21—78no—
70C3×D3×C7—178no—
71C32×D7—1198no—
72C7×C17C3×D3×D718yescomplemented
73C2×C3×C17—1471no—
74D51C3×C7⋊D711yescharacteristic, complemented
75C3×D17—31no—
76C3×D17—491no—
77C3×D17—491no—
78C3×D17—981no—
79D3×C17—491no—
80C2×C72—511no—
81C7⋊D7—31no—
82C7⋊D7—171no—
83C2×C3×D7—3578no—
84D3×D7—1198no—
85C2×D17—1471noHall
86C32×C7D7×D1718yescomplemented
87C3×C17—21no—
88C3×C17D3×C7⋊D711yescharacteristic, complemented
89C3×C17C2×C3×C7⋊D711yescharacteristic, complemented
90C72C3×D3×D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—518no—
92D21—78no—
93C3×D7—218no—
94C3×D7—1198no—
95C3×D7—1198no—
96C3×D7—2388no—
97D3×C7—178no—
98C2×C3×D3—8331noHall
99C2×C17—1471no—
100D17—31no—
101D17—491no—
102C2×D7—3578no—
103C3×C7—28no—
104C3×C7C3×D7×D1718yescomplemented
105C3×C7D21⋊D1718yescomplemented
106C2×C32—8331no—
107C3×D3—171no—
108C3×D3—491no—
109C17C3×D3×C7⋊D711yescharacteristic, complemented, Sylow
110C2×C7—518no—
111D7—218no—
112D7—1198no—
113C22×C3—24991no—
114C2×D3—8331no—
115C32D17×C7⋊D711yescharacteristic, complemented, Sylow
116C7C3×D21⋊D1718yescomplemented
117C2×C3—511no—
118C2×C3—8331no—
119C2×C3—8331no—
120C2×C3—16661no—
121C2×C3—1471no—
122D3—171no—
123D3—491no—
124C22—24991noSylow
125C3—21no—
126C3C3×D17×C7⋊D711yescharacteristic, complemented
127C3D51⋊(C7⋊D7)11yescharacteristic, direct product factor
128C2—511no—
129C2—8331no—
130C2—1471no—
subgroupG/H
center, hypercenterC3D51⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72×C17C22×C3
FrattiniC1G
Fitting, socleC32×C72×C17C22
LCSG ▷ C3×C72×C17
UCSC1 ◁ C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×C7⋊D119C2semidirect
2. C3×C72×D51C2semidirect
3. C3×C17×C3⋊(C7⋊D7)C2semidirect
4. D51⋊(C7⋊D7)C3direct (N × H)
6. C32×C72×C17C22semidirect
7. C17×C3⋊(C7⋊D7)C2×C3semidirect
8. C72×D51C2×C3semidirect
10. C3×C7⋊D119D3semidirect
11. C3×C7⋊D119C2×C3semidirect
17. C3×C72×C17C2×D3semidirect
18. C3×C72×C17C22×C3semidirect
20. C3×C7×D51D7semidirect
23. C7⋊D119C3×D3semidirect
28. C32×C7×C17C2×D7semidirect
29. C3×C3⋊(C7⋊D7)D17semidirect
32. C72×C17C2×C3×D3semidirect
34. C7×D51C3×D7semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17C2×C3×D7semidirect
48. C3×D51C7⋊D7semidirect
52. C3⋊(C7⋊D7)C3×D17semidirect
65. C32×C17C2×C7⋊D7semidirect
67. C3×C72D3×D17semidirect
68. C3×C72C2×C3×D17semidirect
72. C7×C17C3×D3×D7semidirect
74. D51C3×C7⋊D7semidirect
86. C32×C7D7×D17semidirect
88. C3×C17D3×C7⋊D7semidirect
89. C3×C17C2×C3×C7⋊D7semidirect
90. C72C3×D3×D17semidirect
104. C3×C7C3×D7×D17semidirect
105. C3×C7D21⋊D17semidirect
109. C17C3×D3×C7⋊D7semidirect
115. C32D17×C7⋊D7semidirect
116. C7C3×D21⋊D17semidirect
126. C3C3×D17×C7⋊D7semidirect
127. C3D51⋊(C7⋊D7)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×C7⋊D1192
C3×C72×D512
C3×C17×C3⋊(C7⋊D7)2
D51⋊(C7⋊D7)3
C3×D17×C7⋊D73
C3×D21⋊D177
C3×D3×C7⋊D717